Combine all of the ingredients in a 2-quart saucepan over medium-high heat and bring to a boil, stirring often. Once the mixture comes to a boil, reduce the heat to medium-low and allow the pot to simmer until the fruit is tender, about 10 to 15 minutes. Once the fruit is cooked, remove from the heat, and, working in batches, puree the mixture in a blender* (fruit and liquid).
*Use caution when pureeing hot liquids in a blender; only fill the blender 1/3 to halfway full, and remove the feed tube to allow the steam to escape. Hold a damp cloth over the hole of the feed tube to keep the puree from spewing out. (Alternatively, allow the mixture to cool slightly before pureeing.)
When all of the fruit is pureed, transfer to a non-reactive container and allow it to chill thoroughly in the refrigerator before processing in an ice cream maker according to the manufacturer's instructions. Remove the sorbet from the machine and place in a lidded, freezer-safe container and place in the freezer for at least 2 hours before serving.
*When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.
